Update

thiele.mac

@@ -1,64 +0,0 @@
-/*
-Copyright (c) 2020 Thomas Baruchel
-
-Permission is hereby granted, free of charge, to any person obtaining a copy of
-this software and associated documentation files (the "Software"), to deal in
-the Software without restriction, including without limitation the rights to
-use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
-of the Software, and to permit persons to whom the Software is furnished to do
-so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in all
-copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-SOFTWARE.
-*/
-
-
-/*
-
-  In the following example, we use Thiele's interpolation formula
-  for computing the inverse cos function cos^(-1) from 32 points
-  given by the cos function itself.
-
-  We create two vectors:
-    * the vector 'a' contains regularly spaced points in [0..1.55]
-    * the vector 'b' contains cos(x) for each x in vector 'a'
-
-  We set the keepfloat flag to true in order to prevent Maxima
-  to replace the values with rational approximations.
-
-  Then we compute the inverse function by using thiele(b,a);
-  we evaluate this interpolation at 0.5 expecting some value
-  close to pi/3.
-
-(%i18) a:makelist(0.05*i,i,0,31)$
-(%i19) b:makelist(float(cos(0.05*i)),i,0,31)$
-(%i20) keepfloat:true$
-(%i21) subst(x=0.5, thiele(b,a))*3;
-(%o21)                         3.14159265357928
-
-*/
-
-
-/* Thiele's interpolation formula */
-thiele(u, v) := block([rho:makelist(
-                             makelist(v[i], length(v)-i+1),
-                             i, length(v)), a:0],
-                  for i:1 thru length(rho)-1
-                   do rho[i][2]: (u[i]-u[i+1]) / (rho[i][1] - rho[i+1][1]),
-                  for i:3 thru length(rho)
-                   do (for j:1 thru length(rho)-i+1
-                        do rho[j][i]: (u[j]-u[j+i-1])
-                                        / (rho[j][i-1]-rho[j+1][i-1])
-                                        + rho[j+1][i-2]),
-                  rho: rho[1],
-                  for i:length(rho) thru 3 step -1
-                   do a: ratsimp(( 'x - u[i-1])/(rho[i]-rho[i-2]+a)),
-                  ratsimp( v[1] + ( 'x - u[1] ) / (rho[2] + a) ))$